Littlewood's One Circle Problem
It is shown that Littlewood's one circle problem has a negative answer, that is, there exists a continous bounded function f on the unit disk U such that f is not harmonic, but nevertheless for every x is-an-element-of U the equality f(x) = 1/2pi integral-2pi/0 f(x + r(x)e(it))dt holds for some r(x) with 0 < r(x) < 1 - parallel-to x parallel-to.
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349-360
349-360
Cambridge University Press